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Find Missing Angles and Sides Using the Law of Cosines B Step 1: Apply the Law of Cosines to the triangle. Step 2: Select which formula to use. Step 3: Solve for the unknown. Step 2: Select which formula to use. b a a 2 = b 2 + c 2 −2bc⋅cos A b 2 = a 2 + c 2 −2ac⋅cos B c 2 = a 2 + b 2 −2ab⋅cos C C Step 1: Apply the Law of Cosines to the triangle. a 2 = 15.3 2 + 15.2 2 −2 15.3 15.2 ⋅cos 74.7 o Step 3: Solve for the unknown. a 2 =234.09+231.04−465.12⋅cos 74.7 o a 2 =234.09+231.04−122.732 a 2 =342.398 a= 342.398 =18.504=18.5

Find the Angles and Sides Using the Law of Cosines B Step 1: Apply the Law of Cosines to the Triangle. Step 2: Select which formula to use. Step 3: Solve for the unknown. Step 2: Select which formula to use. b 18.5 a a 2 = b 2 + c 2 −2bc⋅cos A b 2 = a 2 + c 2 −2ac⋅cos B c 2 = a 2 + b 2 −2ab⋅cos C C Step 1: Apply the Law of Cosines to the triangle. 15.3 2 = 18.5 2 + 15.2 2 −2 18.5 15.2 ⋅cos B o Step 3: Solve for the unknown. 234.09=342.25+231.04−562.4⋅cos B o 234.09=573.29−562.4⋅cos B o B o =arccos 0.603 = 52.9 o −339.2=−562.4⋅cos B o C o = 180 o − 52.9 o − 74.7 o = 52.4 o 0.603=cos B o

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